1. Field of the Invention
This invention relates to the control of processes and plants that perform those processes. More specifically, the present invention relates to the limiting of the ramp rate of variable under control in order to control stress in a process or plant.
2. Background Information
In control of a plant or process a control system attempts to ramp up and stabilize to a particular variable under control. In some processes or plants (i.e., systems under control) the ramping process may cause stresses which affect the overall yield of the system. The following description describes an example of a problem where the temperature ramping process in a semiconductor furnace may cause stress on a wafer. It should be noted, however, that such problems may occur in other systems and that the example is meant merely to be illustrative and not limiting.
FIG. 1 illustrates a graph of the temperatures on a wafer surface in a semiconductor furnace. Line 110 illustrates the setpoint programmed by the user for the desired temperature on a wafer in a semiconductor furnace. Line 120 illustrates the temperature at the center of the wafer and line 130 illustrates the temperature at the edge of the wafer.
FIG. 2 illustrates a graph of the difference between the temperatures at the edge of the wafer and at the center of the wafer for FIG. 1. Line 210 represents the result of the edge temperature of the wafer minus the center temperature of the wafer (i.e., edge-center temperature).
FIG. 3 illustrates a graph of the difference between the temperatures at the edge of the wafer and at the center of the wafer plotted as (edge-center) temperature versus wafer temperature. Line 310 illustrates the edge temperature of the wafer minus the center temperature of the wafer (i.e., edge-center). As shown, as the (edge-center) 310 ramps up it stabilizes quickly at a quasi-steady state value and then as the ramp rate slows down (i.e., the ramp rate decreases and the temperature of the furnace/wafer stabilizes as illustrated in FIG. 1) the (edge-center) 310 drops off.
Also illustrated in FIG. 3 is stress limit curve 320. The (edge-center) difference may put physical stress on the wafer. Too much stress on the wafer may cause slip faults in the crystals of the wafer. Slip faults are cracks in the crystal structure of a wafer. Slip faults can damage the semiconductor devices being manufactured on the wafer, thus reducing the number of working devices on the wafer (i.e., reducing the yield of the entire semiconductor factory).
The stress limit curve 320 describes an allowable limit. If, at a particular wafer temperature, the (edge-center) temperature 310 is below the stress limit curve 320, slip faults will rarely occur. However, if at any wafer temperature the (edge-center) temperature 310 exceeds the stress limit curve 320, slip faults are much more likely to occur. Therefore, it is desirable to keep the edge-center difference 310 below the stress limit curve 320.
One current attempt to keep the edge-center difference of the wafer temperature below the stress limit curve is to manually adjust the ramp rate. Manual adjustments are mainly made because it is hard to determine the temperatures at the center and edges of the wafer. In general the temperatures at these areas must be estimated because it is difficult to place an actual measurement device close enough to the center of the wafer or the edge of the wafer to measure the actual temperature of those areas.
What is needed is a method and system to limit the ramp rate of a variable under control in order to control stress in a process or plant under control.